Animproved ghost cell method for flow simulation involving static and moving boundary

Abstract

In this paper, an improved ghost cell method is implemented to solve flow problems with static and moving boundary. The two-dimensional unsteady compressible Euler equations are discretized on a fixed Cartesian grid by the finite volume method, and the monotonic upstream-centered scheme for conservation law scheme is adopted to obtain the second-order precision by reconstructing the numerical fluxes computed by the AUSM + (advection upstream splitting method +) scheme. In time discretization, the explicit third-order total-variation-diminishing Runge-Kutta method is considered. To simplify the assignment method for the ghost cells and deal with the slit problem, the cells in the flow field are selected as the mirror points, which avoids complex interpolations. For preventing non-physical solutions when the mirror point is very close to the boundary, the current mirror point will be replaced by another one, which is regarded as the second flow field cell located in the direction away from the boundary. Moreover, properties of a ghost cell along the <i>X</i> and <i>Y</i> direction are computed respectively, and then the final property is obtained by using a weighted average method, where the weight is determined by the distance between the ghost cell and corresponding boundary point. In this method, the selection of mirror points does not change abruptly for adjacent ghost cells, and therefore, no kink occurs. Furthermore, considering the gradient of the variable near the boundary, an extended scheme of the improved ghost cell method is achieved, which can deal with the flow problems with moving boundaries. When computing the property of a ghost cell by using the extended scheme, the result may be wrong if the location of a shock is just between two mirror points. In view of the problem above, a shock monitor is implemented to switch to the appropriate approach, that is, when the monitor detects a shock between mirror points, the extended scheme will be replaced by the original ghost cell method. Two typical test cases are investigated to validate the accuracy of the proposed method. The first test case is the Schardin’s problem, in which a shock impinges on a finite wedge and is reflected and diffracted. The results at different grid sizes are obtained, and good agreement with experiment results as well as the previous numerical results is achieved, which shows that the improved ghost cell method can offer the same precision as the body-fitted grid method. The second test case is the cylinder lift-off problem involving moving boundaries and the slit problem. Good agreement with the previous results of a high-order complex ghost cell method shows that the improved simple ghost cell method can meet the requirement for dealing with flow problems with moving boundaries.